Our analysis has furnished
useful
parametric representations for the general momentum-space conformal \(n\) -point function.
Starting from the generalised simplex Feynman integral of [1]}, [2]},
we showed how all graph polynomials can be obtained from the corresponding Laplacian matrix, or the Gram matrix to which it reduces once momentum conservation has been enforced.
With the graph polynomials to hand, all the usual scalar parametrisations of Feynman integrals can be adapted to represent the simplex solution. Only \(n(n-1)/2\)  integrals over Schwinger parameters remain to be performed – one for each leg of the simplex – in contrast to the \((n-1)(n-2)d/2\)  scalar integrals we started with.
